Minimal Realized Power Systems for Load Frequency Control Using Optimal Theory Based PID Controller

Abstract

The load-frequency control is a matter of interest in power system operation as it addresses the problem of controlling the system in response to the disturbances. A well-known solution to this problem is feedback stabilization through Linear Quadratic Regulator. The observability condition has to be satisfied for the implementation of LQR, but for certain cases of multi-source power systems this criteria fails. Also, to obtain the desired response, proper selection of the weighting matrices Q and R for LQR controller is inevitable. On a trial and error based choice of these matrices, the classical optimal controller may fail to achieve an optimum set point tracking, due to the absence of an integral control action. In this paper, a balanced reduction technique is proposed to obtain a minimal realization of the unobservable system, which makes the optimal control design possible for the control of change in frequency. Thus the paper also applies PID output feedback controller designed through LQR. The impact of reduction for minimal realization and the LQR based PID controller in the frequency stabilization of the considered systems are highlighted in this paper through pertinent cases.

Keywords:

• Load frequency control
• Model order reduction
• Balanced truncation
• Linear quadratic regulator
• Proportional integral derivative controller
• Output feedback PID

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Anju G. Pillai

Anju G Pillai received the Bachelor of Technology in electrical and electronics engineering from the University of Kerala in 2010 and Master of Technology in (power electronics and power systems) from MG University, Kerala in 2013. She is currently pursuing PhD from Rajagiri School of Engineering and Technology under the APJ Abdul Kalam Technological University, Kerala. Her research interests include power system operation control, renewable energy systems and optimization techniques.

Elizabeth Rita Samuel

Elizabeth Rita Samuel received the Bachelor of Technology and the Master of Technology in electrical and electronics engineering from the University of Kerala in 2002 and 2005, respectively. She received her PhD from Gent University, Belgium in electrical engineering in 2015. She is presently working at Rajagiri School of Engineering and Technology under the APJ Abdul Kalam Technological University Kerala. Her current interests are in mathematical modeling, machine learning, model order reduction and control system design. She has publications in several indexed journals and international conference proceedings. Email: [email protected]